Why can't I loop cut a cone?
In layman terms loop cut will only work on geometry with 'clear edge flow' meaning in most if not all cases you should ideally be able to look at it and tell where the cut will go or it should divide your mesh equally into more sections that can be cut again. So it won't work for triangles (3 vertices) or ngons (mesh with more than 4 vertices), What is non-manifold geometry?. There is a simple work around however. Create a cone by adding a cylinder and scaling the top as small as possible without actually letting the vertices overlap, when zoomed out, this is unnoticeable.